Hilbert Space Operators

Starting with elementary operator theory and matrix analysis, this book introduces the basic properties of the numerical range and gradually builds up the whole numerical range theory. Over 400 assorted problems, ranging from routine exercises to published research results, give you the chance to put the theory into practice and test your understanding. Interspersed throughout the text are numerous comments and references, allowing you to discover related developments and to pursue areas of interest in the literature. Also included is an appendix on basic convexity properties on the Euclidean space. Targeted at graduate students as well as researchers interested in functional analysis, this book provides a comprehensive coverage of classic and recent works on the numerical range theory. It serves as an accessible entry point into this lively and exciting research area.

The book concisely presents the fundamental aspects of the theory of operators on Hilbert spaces. The topics covered include functional calculus and spectral theorems, compact operators, trace class a

This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for compact, self-adjoint operators on separable Hilbe

The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger operators

" A treatment of system theory within the context of finite dimensional spaces, this text is appropriate for students with no previous experience of operator theory. The three-part approach, with note

The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrodinger operators

This work is a concise introduction to spectral theory of Hilbert space operators. Its emphasis is on recent aspects of theory and detailed proofs, with the primary goal of offering a modern introduct

The book is a commemorative volume honoring the mathematician Paul R. Halmos (1916-2006), who contributed passionately to mathematics in manifold ways, among them by basic research, by unparalleled ma

The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the pro

Almost ?fteen years later, and there is little change in our motivation. Mathem- ical physics of quantum systems remains a lively subject of intrinsic interest with numerous applications, both actual

This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for compact, self-adjoint operators on separable Hilbe

This book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for compact, self-adjoint operators on separable Hilbe

This self-contained work on Hilbert space operators takes a problem-solving approach to the subject, combining theoretical results with a wide variety of exercises that rang

Physics has long been regarded as a wellspring of mathematical problems. Mathematical Methods in Physics is a self-contained presentation, driven by historic motivations, excellent examples, detailed

Infinite-dimensional Clifford algebras and their Fock representations originated in the quantum mechanical study of electrons. In this book the authors give a definitive account of the various Clifford algebras over a real Hilbert space and of their Fock representations. A careful consideration of the latter's transformation properties under Bogoliubov automorphisms leads to the restricted orthogonal group. From there, a study of inner Bogoliubov automorphisms enables the authors to construct infinite-dimensional spin groups. Apart from assuming a basic background in functional analysis and operator algebras, the presentation is self-contained with complete proofs, many of which offer a fresh perspective on the subject. The book will therefore appeal to a wide audience of graduate students and researchers in mathematics and mathematical physics.

This classic textbook introduces linear operators in Hilbert Space, and presents the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. Invaluable for every math

Professor Retherford's aim in this book is to provide the reader with a virtually self-contained treatment of Hilbert space theory, leading to an elementary proof of the Lidskij trace theorem. He assumes the reader is familiar with only linear algebra and advanced calculus, and develops everything needed to introduce the ideas of compact, self-adjoint, Hilbert-Schmidt and trace class operators. Many exercises and hints are included, and throughout the emphasis is on a user-friendly approach. Advanced undergraduates and graduate students will find that this book presents a unique introduction to operators and Hilbert space.

Professor Retherford's aim in this book is to provide the reader with a virtually self-contained treatment of Hilbert space theory, leading to an elementary proof of the Lidskij trace theorem. He assumes the reader is familiar with only linear algebra and advanced calculus, and develops everything needed to introduce the ideas of compact, self-adjoint, Hilbert-Schmidt and trace class operators. Many exercises and hints are included, and throughout the emphasis is on a user-friendly approach. Advanced undergraduates and graduate students will find that this book presents a unique introduction to operators and Hilbert space.

Gallone presents students, academics, and researchers with an investigation of the mathematical foundations and theory of non-relativistic quantum mechanics. The author has organized the main body of

This lively and accessible book describes the theory and applications of Hilbert spaces and also presents the history of the subject to reveal the ideas behind theorems and the human struggle that led to them. The authors begin by establishing the concept of 'countably infinite', which is central to the proper understanding of separable Hilbert spaces. Fundamental ideas such as convergence, completeness and dense sets are first demonstrated through simple familiar examples and then formalised. Having addressed fundamental topics in Hilbert spaces, the authors then go on to cover the theory of bounded, compact and integral operators at an advanced but accessible level. Finally, the theory is put into action, considering signal processing on the unit sphere, as well as reproducing kernel Hilbert spaces. The text is interspersed with historical comments about central figures in the development of the theory, which helps bring the subject to life.

Linear operators in Hilbert spaces play a fundamental role in the formulation of quantum theory. With complete proofs and numerous exercises, this book offers a self-contained presentation of the most

Starting with a definition of Hilbert space and its geometry, this text explores the general theory of bounded linear operators, the spectral analysis of compact linear operators, and unbounded self-a

A rigorous, critical presentation of the basic mathematics of nonrelativistic quantum mechanics, this text is suitable for courses in functional analysis at the advanced undergraduate and graduate lev

This textbook is an introduction to the theory of Hilbert space and its applications. The notion of Hilbert space is central in functional analysis and is used in numerous branches of pure and applied mathematics. Dr Young has stressed applications of the theory, particularly to the solution of partial differential equations in mathematical physics and to the approximation of functions in complex analysis. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained. It is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). Thus it will make an excellent first course in Hilbert space theory at either undergraduate or graduate level and will also be of interest to electrical engineers and physicists, particularly those involved in control theory and filter design.

This concise introductory treatment consists of three chapters: The Geometry of Hilbert Space, The Algebra of Operators, and The Analysis of Spectral Measures. Author Paul R. Halmos notes in the Prefa

This book deals with various aspects of commutants and reducing subspaces of multiplication operators on the Bergman space, along with relevant von Neumann algebras generated by these operators, which